Hydrologic phenomena are in reality stochastic in nature; that is, their behavior changes with the time in accordance with the law of probability as well as with the sequential relationship between the occurrences of the phenomenon. In order to analyze the hydrologic phenomenon, a mathematic model of the stochastic hydrologic system to simulate the phenomenon must be formulated. In this study, a watershed is treated as the stochastic hydrologic system whose components of precipitation, runoff, storage and evapotranspiration are simulated as stochastic processes by time series models to be determined by correlograms and spectral analysis. The hydrologic system model is then formulated on the basis of the principle of conservation of mass and composed of the component stochastic processes. To demonstrate the practical application of the method of analysis so developed, the upper Sangamon River basin above Monticello in east central Illinois is used as the sample watershed. The watershed system model so formulated can be employed to generate stochastic streamflows for practical use in the analysis of water resources systems. This is of particular value in the economic planning of water supply and irrigation projects which is concerned with the long-range water yield of the watershed.